Apparatus and method for recording fresnel holograms

ABSTRACT

An apparatus for producing a hologram of an object includes a light source that emits an incoherent electromagnetic wave toward the object, and a masking device configured to display a mask, receive the incoherent electromagnetic wave emitted toward the object, mask the received incoherent electromagnetic wave according to the displayed mask, and produce a masked electromagnetic wave. The apparatus also includes an image recording device configured to capture an image of the masked electromagnetic wave, and a processing device configured to convert the image of the masked electromagnetic wave into the hologram of the object. A method for producing a hologram of an object is also described.

CROSS--REFERENCE TO RELATED APPLICATIONS

This application is a continuation of application Ser. No. 13/184,279,filed Jul. 15, 2011, which is a continuation of application Ser. No.12/022,892, filed Jan. 30, 2008, which claims priority to ProvisionalU.S. Patent Application No. 60/887,273, filed Jan. 30, 2007, the entirecontents of each of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION Field of the Invention

This invention relates to an apparatus and method for recordinginformation, such as Fresnel holograms, and in particular, to recordinglensless digital incoherent Fresnel holograms using a mask, such as anabsorption-only mask.

Discussion of the Background

Holograms recorded by incoherent light open many new applications likeoutdoor and astronomical holography (J. B. Breckinridge,“Two-Dimensional White Light Coherence Interferometer,” Appl. Opt. 13,2760 (1974)) and fluorescence holographic microscopy (G. Indebetouw, A.El Maghnouji, R. Foster, “Scanning holographic microscopy withtransverse resolution exceeding the Rayleigh limit and extended depth offocus,” J. Opt. Soc. Am. A 22, 892-898 (2005)). The oldest methods ofrecording incoherent holograms have made use of the property that everyincoherent object is composed of many source points each of which isself spatial coherent and therefore can create an interference patternwith light coming from the point's mirrored image. Under this generalprinciple there are various types of holograms (J. B. Breckinridge,“Two-Dimensional White Light Coherence Interferometer,” Appl. Opt. 13,2760 (1974)) (A. W. Lohmann, “Wavefront Reconstruction for IncoherentObjects,” J. Opt. Soc. Am. 55, 1555-1556 (1965)) (G. Sirat, D. Psaltis,“Conoscopic holography,” Optics Letters, 10, 4-6 (1985)) includingFourier (J. B. Breckinridge, “Two-Dimensional White Light CoherenceInterferometer,” Appl. Opt. 13, 2760 (1974)) (G. W. Stroke and R. C.Restrick, “Holography with Spatially Incoherent Light,” Appl. Phys.Lett. 7, 229 (1965)) and Fresnel holograms (G. Cochran, “New method ofmaking Fresnel transforms,” J. Opt. Soc. Am. 56, 1513-1517 (1966)) (P.J. Peters, “Incoherent holography with mercury light source,” Appl.Phys. Lett. 8, 209-210 (1966)). The process of beam interfering demandshigh levels of light intensity, extreme stability of the optical setupand a relatively narrow bandwidth light source. These limitations haveprevented holograms from becoming widely used for many practicalapplications.

More recently two groups of researchers have proposed to computeholograms of 3-D incoherently illuminated objects from a set of imagestaken from different points of view. (Y. Li, D. Abookasis and J. Rosen,“Computer-generated holograms of three-dimensional realistic objectsrecorded without wave interference,” Appl. Opt. 40, 2864-2870 (2001))(Y. Sando, M. Itoh, and T. Yatagai, “Holographic three-dimensionaldisplay synthesized from three-dimensional Fourier spectra of realexisting objects,” Opt. Lett 28, 2518-2520 (2003)) This method, althoughit shows promising prospects, is relatively slow since it is based oncapturing tens of images of the subject scene from different viewangles.

Another method is called scanning holography (G. Indebetouw, A. ElMaghnouji, R. Foster, “Scanning holographic microscopy with transverseresolution exceeding the Rayleigh limit and extended depth of focus,” J.Opt. Soc. Am. A. 22, 892-898 (2005)) (Poon T.-C., “Three-dimensionalimage processing and optical scanning holography,” Adv. in Imag. & Elec.Phys. 126, 329-350 (2003)) in which a Fresnel Zone Plate (FZP) patternis scanned across the object such that at each and every scanningposition the light intensity is integrated by a point detector. Theoverall process yields a Fresnel hologram obtained as a correlationbetween the object and FZP patterns. However the scanning process is arelatively slow and is done by mechanical movements. A similarcorrelation is actually done also in the present work; however, unlikethe case of scanning holography, we propose here a correlation withoutmovement.

Mertz and Young (L. Mertz and N. O. Young, “Fresnel transformations ofimages,” in Proceedings of Conference on Optical Instruments andTechniques, K. J. Habell, ed. (Chapman and Hall, London 1961) p. 305)already proposed holographic photography based on correlation withoutmovement between object and FZPs. However, their process relies ongeometrical optics, which cannot yield good imaging results in theoptical regime. On the contrary, our suggested correlator forimplementing the holographic recording is valid in the optical regime,since its operation principle is based on the diffraction theory (J.Goodman, Introduction to Fourier Optics, 2^(nd) ed., McGraw-Hill, NewYork, 1996, pp. 63-95 (Chapter 4)).

SUMMARY OF THE INVENTION

Accordingly, one object of this invention is to provide a novelapparatus for producing a hologram of an object, the apparatuscomprising: a light source that emits an incoherent electromagnetic wavetoward the object; a masking device configured to display a mask,receive the incoherent electromagnetic wave emitted toward the object,mask the received incoherent electromagnetic wave according to thedisplayed mask, and produce a masked electromagnetic wave; an imagerecording device configured to capture an image of the maskedelectromagnetic wave; and a processing device configured to convert theimage of the masked electromagnetic wave into the hologram of theobject.

Another object of this invention is to provide a novel method forproducing a hologram of an object, the method comprising: emitting anincoherent electromagnetic wave toward the object; displaying adisplayed mask; receiving the incoherent electromagnetic wave emittedtoward the object; masking the received incoherent electromagnetic waveaccording to the displayed mask to produce a masked electromagneticwave; capturing an image of the masked electromagnetic wave; convertingthe image of the masked electromagnetic wave into the hologram of theobject.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete appreciation of the invention and many of the attendantadvantages thereof will be readily obtained as the same becomes betterunderstood by reference to the following detailed description whenconsidered in connection with the accompanying drawings, wherein:

FIG. 1 is a schematic representation of an embodiment of the present.invention; and

FIG. 2 is a schematic representation of another embodiment of thepresent invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention includes a new method of recording digitalholograms under incoherent illumination, and corresponding apparatusesthat may be configured to record digital holograms under incoherentillumination. According to an embodiment of the invention, light istransmitted through, or reflected from a three-dimensional (3-D) object,propagated through an absorption Fresnel zone plate (FZP), and recordedby a digital camera. In one embodiment, five holograms are recordedsequentially, each for a different phase factor of the FZP, and the fiverecorded holograms are superposed such that the result is a complexvalued Fresnel hologram. When the hologram is reconstructed, 3-Dproperties of the object are revealed.

Thus, the present invention includes a lensless method of recordingdigital Fresnel holograms under incoherent illumination. The presentinvention is an extension of the FINCH holographic technique which wehave previously described (J. Rosen, and G. Brooker “Digital spatiallyincoherent Fresnel holography,” Accepted for publication in Opt. Lett)(J. Rosen, and. G. Brooker “Fluorescence incoherent color holography,”Submitted for publication in Opt. Exp. (2007)) (Patents pending). In anembodiment of a method or apparatus according to the present invention,incoherent light transmitted through, or reflected from, a 3-D objectpropagates through an absorption-only FZP and is recorded by a digitalcamera. Five holograms may be recorded sequentially (or simultaneouslyunder certain conditions) each with a different phase factor of the FZP.Information representing the five recorded holograms are superposedusing a superposing process (for example using dedicated hardware orusing a general purpose computing device such as a computer) such thatthe result is a complex valued Fresnel hologram. As we show in thefollowing, the 3-D properties of the object are revealed byreconstructing this hologram using a digital reconstructing process.

The setup is lensless and contains absorption-only FZPs. Theseproperties make the system suitable for operating with waves other thanelectromagnetic waves, or with electromagnetic waves in spectral regimesother than the visible light regime, in which it is impossible orextremely difficult to implement lenses and other phase elements. Forelectromagnetic waves the present system can be applied to x-rays, andtherefore the method can be an important tool for medical imaging. Thepresent invention may also be applied to 3D x-ray imaging, and elementsof the inventive apparatus or method may be configured such that theradiation is transferred from the source through the semi-absorptionobject, rather than reflected from the object as we have shown inprevious demonstrations of FINCH. (J. Rosen, and G. Brooker “Digitalspatially incoherent Fresnel holography,” Accepted for publication inOpt. Lett) (J. Rosen, and G. Brooker “Fluorescence incoherent colorholography,” Submitted for publication in Opt. Exp. (2007))

FIG. 1 shows a schematic view of a first embodiment of a lensless FINCHapparatus according to the present invention. The lensless FINCHapparatus includes an incoherent source 10 that illuminates a 3-D object12 and the transmitted light 14 is captured by a CCD camera 16 afterpassing through the object 12 and reflecting from one or more reflectiveFZPs 18 displayed by a spatial light modulator (SLM) 20, or on anotherdevice that can be configured to change from one FZP to another.

Following is analysis of the inventive apparatus to demonstrate that theapparatus may produce a hologram of a 3D object. The apparatus can beanalyzed as an incoherent correlator, where the FZP function isconsidered as a part of the system's transfer function. Alternatively,it may be more useful to analyze the apparatus as an incoherentinterferometer, where the grating displayed on the SLM (i.e., the FZP)is considered as a beam splitter. In particular, the apparatus may beanalyzed by following its response to an input object of a singleinfinitesimal point. Based on the point spread function (PSF) of theapparatus, the operation of the apparatus may be analyzed for anygeneral object. Analysis of a beam originated from narrow bandinfinitesimal point source is done using Fresnel diffraction theory (J.Goodman, Introduction to Fourier Optics, 2^(nd) ed., McGraw-Hill, NewYork, 1996, pp. 63-95 (Chapter 4)) since such a source is coherent bydefinition.

Referring to the embodiment of FIG. 1, a Fresnel hologram of a pointobject is obtained on a plane of the CCD 16 that is distance d from theSLM 20, when a reflection function R(X_(D), Y_(D)) is real and positivein the form of,

$\begin{matrix}\begin{matrix}{{R\left( {x_{D},y_{D}} \right)} = {\frac{1}{2} + {\frac{1}{4}{\exp \left\lbrack {{\frac{i\; \pi}{\lambda \; f}\left( {x_{D}^{2} + y_{D}^{2}} \right)} + {i\; \theta}} \right\rbrack}} + {\frac{1}{4}{\exp \left\lbrack {{{- \frac{i\; \pi}{\lambda \; f}}\left( {x_{D}^{2} + y_{D}^{2}} \right)} - {i\; \theta}} \right\rbrack}}}} \\{{= {\frac{1}{2} + {\frac{1}{4}{Q\left( \frac{1}{f} \right)}\mspace{11mu} \exp \; \left( {i\; \theta} \right)} + {\frac{1}{4}{Q\left( {- \frac{1}{f}} \right)}{\exp \left( {{- i}\; \theta} \right)}}}},}\end{matrix} & (1)\end{matrix}$

Where λ is the central wavelength, and for reasons of increased clarity,the quadratic phase function is designated by the function Q such thatQ(b)=exp[iπb/λ(x²+y²)].

The angle θ plays an important role later in the computation process inorder to get rid of the twin images and the bias terms.

A point source located at the point (0, 0, z_(s)) a distance L=2f−z_(s),from the SLM 20 induces on the SLM plane a diverging spherical wave ofthe form of Q(1/L). Right after the SLM 20, which has a reflection (ortransmission) function given in Eq. (1) , the complex amplitude of thewave is related to

Q{1/(L)}[0.5+0.25·Q(−1/f)exp(iθ)+0.25·Q(−1/f)exp(i θ)].

Finally, in the CCD plane a distance d from the FZP, the intensity ofthe recorded hologram of a point is,

$\begin{matrix}\begin{matrix}{{H_{P}\left( {x,y} \right)} = {A{{{\frac{1}{2}{Q\left\lbrack \frac{1}{L} \right\rbrack}} + {\frac{1}{4}{Q\left\lbrack \frac{f + L}{{Lf} + {df} + {Ld}} \right\rbrack}{\exp \left( {i\; \theta} \right)}} +}}}} \\{{\frac{1}{4}{Q\left\lbrack \frac{f - L}{{Lf} + {df} - {Ld}} \right\rbrack}{\exp \left( {{- i}\; \theta} \right)}}}^{2} \\{= {A{{{\frac{1}{2}{Q\left\lbrack \left( {{2f} - z + d} \right)^{- 1} \right\rbrack}} + {\frac{1}{4}{Q\left\lbrack \left( {\frac{f\left( {{2f} - z} \right)}{{3f} - z} + d} \right)^{- 1} \right\rbrack}{\exp \left( {i\; \theta} \right)}} +}}}} \\{{{\frac{1}{4}{Q\left\lbrack \left( {\frac{- {f\left( {{2f} - z} \right)}}{f - z} + d} \right)^{- 1} \right\rbrack}{\exp \left( {{- i}\; \theta} \right)}}}^{2} \propto {6 +}} \\{{{2{Q\left\lbrack S_{1} \right\rbrack}{\exp \left( {{- i}\; \theta} \right)}} + {2{Q\left\lbrack {- S_{1}} \right\rbrack}{\exp \left( {i\; \theta} \right)}} + {2{Q\left\lbrack S_{2} \right\rbrack}{\exp \left( {i\; \theta} \right)}} +}} \\{{{2{Q\left\lbrack {- S_{2}} \right\rbrack}{\exp \left( {{- i}\; \theta} \right)}} + {{Q\left\lbrack S_{3} \right\rbrack}{\exp \left( {2i\; \theta} \right)}} + {{Q\left\lbrack {- S_{3}} \right\rbrack}{\exp \left( {{- 2}i\; \theta} \right)}}}}\end{matrix} & (2) \\{where} & \; \\{{S_{1} = \frac{- L^{2}}{\left( {L + d} \right)\left( {{Lf} + {df} + {Ld}} \right)}},{S_{2} = \frac{L^{2}}{\left( {L + d} \right)\left( {{Lf} + {df} - {Ld}} \right)}},{S_{3} = {\frac{2L^{2}f}{\left( {{Lf} + {df}} \right)^{2} - {L^{2}d^{2}}}.}}} & (3)\end{matrix}$

Eq. (2) has seven different terms where for a good holographic recordingonly one term of quadratic function (Q function) should remain after thesuperposition. Otherwise, reconstructing the hologram given in Eq. (2)with its all seven terms will affect an overlap between all sevendifferent images. Looking closely in Eq. (2) , there are two terms withthe constant 2exp(iθ) and two terms with 2exp(−iθ). Therefore, weconclude that at least five holograms with different values of θ'sangles are needed to be recorded, and to be superposed together, inorder to get a single term out of the seven. Furthermore, thesuperposition can yield only one of the two terms Q[S₃] or Q[−S₃].

In order to remain with a single correlation term out of the seven termsgiven in Eq. (4) , we follow the usual procedure of phase stepping(Patents pending), but with five holograms. Five holograms of the sameobject are recorded each of which with a different phase constant θ. Thefinal hologram H_(F) is a superposition according to the following,

$\begin{matrix}{{H_{F}\left( {x,y} \right)} = {\frac{\left\lbrack {{{H_{1}\left( {x,y} \right)}{\exp \left( {i\; \theta_{1}} \right)}} - {{H_{5}\left( {x,y} \right)}{\exp \left( {i\; \theta_{5}} \right)}}} \right\rbrack \left( {{A_{3}B_{2}} - {A_{2}B_{3}}} \right)}{\left\lbrack {{\exp \left( {2\; i\; \theta_{1}} \right)} - {\exp \left( {2\; i\; \theta_{5}} \right)}} \right\rbrack} - \frac{\left\lbrack {{{H_{2}\left( {x,y} \right)}{\exp \left( {i\; \theta_{2}} \right)}} - {{H_{5}\left( {x,y} \right)}{\exp \left( {i\; \theta_{5}} \right)}}} \right\rbrack \left( {{A_{3}B_{1}} - {A_{1}B_{3}}} \right)}{\left\lbrack {{\exp \left( {2\; i\; \theta_{2}} \right)} - {\exp \left( {2\; i\; \theta_{5}} \right)}} \right\rbrack} - \frac{\left\lbrack {{{H_{3}\left( {x,y} \right)}{\exp \left( {i\; \theta_{3}} \right)}} - {{H_{5}\left( {x,y} \right)}{\exp \left( {i\; \theta_{5}} \right)}}} \right\rbrack \left( {{A_{3}B_{2}} - {A_{2}B_{1}}} \right)}{\left\lbrack {{\exp \left( {2\; i\; \theta_{3}} \right)} - {\exp \left( {2\; i\; \theta_{5}} \right)}} \right\rbrack} - \frac{\begin{matrix}\left\lbrack {{{H_{4}\left( {x,y} \right)}{\exp \left( {i\; \theta_{4}} \right)}} - {{H_{5}\left( {x,y} \right)}{\exp \left( {i\; \theta_{5}} \right)}}} \right\rbrack \\\left( {{A_{2}B_{1}} - {A_{2}B_{3}} - {A_{3}B_{1}} + {A_{1}B_{3}}} \right)\end{matrix}}{\left\lbrack {{\exp \left( {2\; i\; \theta_{4}} \right)} - {\exp \left( {2\; i\; \theta_{5}} \right)}} \right\rbrack}}} & (4)\end{matrix}$

where H_(k) is the kth recorded hologram with the phase constant θ_(k),and the constants are,

$\begin{matrix}{{A_{k} = {\frac{{\exp \left( {i\; \theta_{k}} \right)} - {\exp \left( {i\; \theta_{5}} \right)}}{{\exp \left( {2i\; \theta_{k}} \right)} - {\exp \left( {2i\; \theta_{5}} \right)}} - \frac{{\exp \left( {i\; \theta_{4}} \right)} - {\exp \left( {i\; \theta_{5}} \right)}}{{\exp \left( {2i\; \theta_{4}} \right)} - {\exp \left( {2i\; \theta_{5}} \right)}}}}{B_{k} = {\frac{{\exp \left( {{- i}\; \theta_{k}} \right)} - {\exp \left( {{- i}\; \theta_{5}} \right)}}{{\exp \left( {2i\; \theta_{k}} \right)} - {\exp \left( {2i\; \theta_{5}} \right)}} - \frac{{\exp \left( {{- i}\; \theta_{4}} \right)} - {\exp \left( {{- i}\; \theta_{5}} \right)}}{{\exp \left( {2i\; \theta_{4}} \right)} - {\exp \left( {2i\; \theta_{5}} \right)}}}}} & (5)\end{matrix}$

The intensities of the five recorded holograms of an object aresuperposed according to Eq. (5). The result is an integral of the PSF,one quadratic phase function resulting from Eq. (5) , over all objectintensity g(x_(s), Y_(s), z_(s)), as follows

$\begin{matrix}{{H\left( {x,y} \right)} \cong {A{\int{\int{\int{{g\left( {x_{s},y_{s},z_{s}} \right)}\exp \left\{ {{\frac{i\; \pi \; {S_{3}(z)}}{\lambda}\left\lbrack {\left( {x + \frac{{ax}_{s}}{f}} \right)^{2} + \left( {y + \frac{{ay}_{s}}{f}} \right)^{2}} \right\rbrack} + {i\; \theta}} \right\} {dx}_{s}{dy}_{s}{dz}_{s}}}}}}} & (6)\end{matrix}$

Eq. (4) is a correlation between an object and a quadratic phase,z-dependent, function, which means that the recorded hologram is indeeda Fresnel hologram.

A 3-D image s(x, y, z) can be reconstructed from H_(F)(x, y) bycalculating the Fresnel propagation formula, as follows,

$\begin{matrix}{{{s\left( {x,y,z} \right)} = {{H_{F}\left( {x,y} \right)}*{\exp \left\lbrack {\frac{i\; \pi}{\lambda \; z}\left( {x^{2} + y^{2}} \right)} \right\rbrack}}},} & (7)\end{matrix}$

where the asterisk denotes a 2-D convolution.

There are numerous modifications based upon the lensless holographicconcept and proof described above which are possible and are included inthe present invention. For example, there are numerous other embodimentsbased on this invention that may speed up the image capture. Theinvention also includes related methods to reduce the number ofholographic images which are needed to create a single hologram.Furthermore, the present invention also includes simultaneouslycapturing plural images and holograms, as described above, by splittingthe captured image beam into five beams and simultaneously capturing the5 described holograms.

Thus, the apparatus as described above, and a corresponding method, mayrecord incoherent holograms of realistic 3-D objects using onlyabsorption masks. Since the lensless FINCH system has only a singlechannel it does not demand. complicated alignment. However, theinvention also applies to operation using plural channels. Theadvantages of the present invention may be applied to the design of aportable and low cost holographic camera for electromagnetic waves otherthan just the visible light, which might be useful for variousapplications in medical imaging. (Patents pending)

FIG. 2 is a schematic diagram of an alternative embodiment of thelensless FINCH apparatus. The embodiment of FIG. 2 is similar to that ofFIG. 1. However, in FIG. 2, an SLM 24 configured to produce transmissiveFZPs 22 replaces the SLM 20 configured to produce reflective FZPs 18.

Numerous modifications and variations of the present invention arepossible in light of the above teachings therefore to be understood thatwithin the scope of the appended claims, the invention may be practicedotherwise than as specifically described herein.

1-20. (canceled)
 21. An apparatus for producing a hologram of an object,the apparatus comprising: a device configured to receive an incoherentelectromagnetic wave reflected from or transmitted through athree-dimensional object, and propagate the received incoherentelectromagnetic wave through an absorption-only Freznel Zone Plate(FZP); an image recording device configured to capture an image of thepropagated electromagnetic wave; and a processing system comprising atleast one processor, the processing system being configured to generatethe hologram of the three-dimensional object based on the image of themasked electromagnetic wave captured by the image recording device. 22.The apparatus of claim 21, wherein the incoherent electromagnetic waveis an x-ray wave.
 23. The apparatus of claim 21, wherein the incoherentelectromagnetic wave is a visible light.
 24. The apparatus of claim 21,wherein the device is configured to display an absorption mask.
 25. Theapparatus of claim 21, wherein the device is configured to display aplurality of different absorption masks over a predetermined timeperiod.
 26. The apparatus of claim 21, wherein the device is configuredto display a reflective absorption mask.
 27. The apparatus of claim 21,wherein the device is configured to display a transmissive absorptionmask.
 28. The apparatus of claim 21, wherein the device includes aspatial light modulator (SLM) configured to change a displayed mask fromone Fresnel Zone Pattern to another.
 29. The apparatus of claim 21,wherein the device is configured to propagate the received incoherentelectromagnetic wave through Fresnel Zone Patterns having a differentphase factor, and the processing system generates the hologram using aplurality of images captured by the image recording device, each imagebeing captured while the received incoherent electromagnetic wave ispropagated through a different phase factors of the Fresnel ZonePattern.
 30. A method for producing a hologram of a three-dimensionalobject, the method comprising: receiving an incoherent electromagneticwave reflected from or transmitted through the three-dimensional object;propagating the received incoherent electromagnetic wave through anabsorption-only Freznel Zone Plate (FZP); capturing an image of thepropagated electromagnetic wave; and generate the hologram of thethree-dimensional object based on the image of the captured maskedelectromagnetic wave.
 31. The method of claim 30, wherein the incoherentelectromagnetic wave is an x-ray wave.
 32. The method of claim 30,wherein the incoherent electromagnetic wave is a visible light.
 33. Themethod of claim 30, wherein the device includes an absorption mask. 34.The method of claim 30, wherein the device includes a reflectiveabsorption mask.
 35. The method of claim 30, wherein the device includesa transmissive absorption mask.
 36. An apparatus for producing ahologram of an object, the apparatus comprising: means for producing aelectromagnetic wave by propagating an incoherent electromagnetic wavereflected from or transmitted through three-dimensional object throughan absorption-only Freznel Zone Plate (FZP); an image recording deviceconfigured to capture an image of the propagated electromagnetic wave;and a processing system comprising at least one processor, theprocessing system being configured to generate a hologram based on theimage of the propagated electromagnetic wave captured by the imagerecording device.